CW-E-对称可微区间值函数及其在广义凸区间值优化问题中的应用  

CW-E-symmetric differentiable interval-valued functions and its applications in generalized convex interval-valued optimization problems

作　　者：李慧云 叶国菊[1] 刘尉[1] 赵大方 LI Huiyun;YE Guoju;LIU Wei;ZHAO Dafang(College of Science,Hohai University,Nanjing 210098,China;School of Mathematics and Statistics,Hubei Normal University,Huangshi 435000,China)

机构地区：[1]河海大学理学院,江苏南京210098 [2]湖北师范大学数学与统计学院,湖北黄石435000

出　　处：《湖北大学学报（自然科学版）》2023年第4期478-486,共9页Journal of Hubei University：Natural Science

基　　金：江苏省自然科学基金(BK20180500);湖北省教育厅重点项目(D20192501)资助。

摘　　要：借助向量值映射E:R n→R n,这里R n是n维实数空间,首先提出一类新的CW-E-对称可微区间值函数,将不可微区间值函数转换成可微函数,进而研究该类函数性质;其次在区间CW-序关系,引入CW-E-预不变凸区间值函数和CW-E-对称不变凸区间值函数的定义,并在CW-E-对称可微下,研究CW-E-预不变凸区间值函数和CW-E-对称不变凸区间值函数的关系.最后,作为应用,研究广义不变凸区间值优化问题的E-最优性条件,并举例验证了结果的有效性.In this paper,we firstly introduced a new class of CW-E-symmetric differentiable interval-valued functions under an operator E:R n→R n,and this derivative transformed a non-differentiable interval-valued function to a differentiable one.Then we presented the definitions of CW-E-preinvex and CW-E-symmetric invex interval-valued functions with the help of CW-order between intervals.The relationships between CW-E-preinvex and CW-E-symmetric invex interval-valued functions were given while the interval-valued functions were CW-E-symmetric differentiable.At last,the optimality conditions in generalized invex interval-valued optimization problems were studied and an example was illustrated to show the rationality of our results.

关 键 词：CW-E-对称可微区间值函数 广义不变凸性 区间值优化问题 E-最优性条件 

分 类 号：O172.1[理学—数学] O224[理学—基础数学]